Statistical
LOGEST Function
Calculates an exponential curve that fits your data and returns an array that describes the curve.
by
Charley Kyd, MBA Microsoft Excel MVP, 20052014
The Father of Spreadsheet Dashboard Reports

The LOGEST function fits an exponential curve—that is, a
growthrate curve—to your data and returns one or more values
that describe the curve. When you want more than one value, you
must enter it as an array or your must include it in an INDEX
function.
Syntax
LOGEST(known_y's, known_x's, const,
stats)

known_y's
Required. The range or array of y values you already know in
the relationship y = b*m^x. (From another perspective, a
chart typically displays the same "y" values in the vertical
axis.)

known_x's
Optional. The range or array of x values you typically know
in the relationship y = b*m^x. (From another perspective,
"x" values are frequently date serial numbers, counters, or
other numeric categories.) If 'known_x's' is omitted, it is
assumed to be the array {1,2,3,...} that is the same size as
'known_y's'.

const
Optional. A logical value that specifies whether to force
the constant b to equal 1.

If const is TRUE or omitted,
then b is calculated normally.

If const is FALSE, b is set
equal to 1, and the mvalues are fitted to y = m^x

stats
Optional. A logical value that specifies whether to return
additional regression statistics.

If stats is FALSE or omitted,
LOGEST returns only the mcoefficients and the constant
b, as shown in the first two rows of the following
table.

If stats is TRUE, LOGEST
returns these regression statistics as an array:
Row 
Col 
Name 
Description 
1 
1 
m 
The growth rate of the curve 
1 
2 
b 
The yintercept (which
is the yintercept) of the curve 
2 
1 
se 
The standard error
value for m 
2 
2 
seb 
The standard error value for b 
3 
1 
R^{2} 
The coefficient of determination 
3 
2 
sey 
The standard error of the y estimate 
4 
1 
F 
The F statistic 
4 
2 
df 
The degrees of freedom 
5 
1 
ssreg 
The regression sum of squares 
5 
2 
ssresid 
The residual sum of squares 
Applies To
Excel 2003 and above
Remarks
When you have only one independent xvariable, and if you
enter a LOGEST formula normally, it returns the "m" value, which
is equal to one plus the growth rate of the fitted curve.
When you have only one independent xvariable, you can obtain
yintercept (b) values directly by using the formula...
=INDEX(LOGEST(known_y's,known_x's),2)
Similarly, this formula also will return the yintercept (b)
values...
=GROWTH(known_y's, known_x's, 0)
Examples
The following examples use this data:
Other ExcelUser Information
Other Help
